Field of the Invention
The present disclosure relates generally to image processing and, more specifically, to a system and method for image processing using highly undersampled imaging data.
Description of the Related Art
Spin-spin (T2) relaxation is one of the main contrast mechanisms in MRI. Although most clinical applications use qualitative (visual) information derived from T2-weighted images, there is an increasing interest in T2 mapping (1-10).
Because single-echo spin-echo T2 mapping requires long acquisition times, its translation to the clinic has been limited by its time inefficiency. In order to reduce the acquisition times it is customary to use multi-echo spin-echo (MESE) pulse sequences, where several echo time (TE) points are acquired per repetition time (TR) period by using a train of 180° refocusing pulses after the initial 90° excitation pulse. To further accelerate T2 data acquisition, a fast (or turbo) spin-echo approach where several k-space lines of data are acquired per TR period is commonly used. For the sake of speed in T2 mapping (while maintaining high spatial and temporal resolution), the use of TE data sets that are undersampled in k-space has been proposed in conjunction with a fast spin-echo approach. Several algorithms have been described to recover T2 information from these highly reduced TE data sets (11-16). Recently, the focus has been on model-based T2 mapping algorithms. Doneva et al. proposed to exploit the temporal sparsity of the exponential decay while reconstructing all TE images under the framework of compressed sensing (13, 16). Block et al. proposed a model-based algorithm for radial fast-spin-echo acquisitions to directly reconstruct I0 and R2 (1/T2) maps from the measured k-space data (11). Because I0 and R2 values have very different scales the gradient-based minimization process requires a scaling factor which needs to be fine-tuned for accurate T2 estimation (12). Our group has recently developed the REPCOM (REconstruction of Principal COmponent coefficient Maps) algorithm which linearizes the signal model using principal component analysis (PCA). REPCOM exploits the spatial and temporal sparsity of the TE images, and provides accurate T2 estimates from highly undersampled data without the need of a scaling factor for the fitted parameters.
The algorithms described above, including REPCOM, rely on the assumption that the signal follows an exponential decay. However, in MESE acquisitions the decay is generally contaminated by indirect echoes (echoes leading to signal generation after more than one refocusing pulse such as stimulated echoes) including differences in the signal intensities between even and odd echoes, thus, altering the single exponential nature of the T2 decay observed in a single-echo spin-echo experiment. The indirect echoes are the result of refocusing pulses not attaining the ideal 180° flip angle (FA) due to nonrectangular slice profiles, static (B0) and transmit field (B1) inhomogeneity, and B1 calibration errors (17).
To alleviate the pulse imperfection due to nonrectangular slice profiles, a thick refocusing slice technique has been proposed by Pell et al. (5). This technique employs a refocusing slice that is thicker than the excitation slice. B0 and B1 inhomogeneity, and calibration errors, however, are not corrected for by this approach. Echo editing techniques that use crusher gradients around the refocusing pulses have also been proposed to reduce the signal resulting from pathways leading to indirect echoes (18-20). However, not all pathways can be crushed effectively and the method has only been demonstrated with non-selective refocusing pulses, which limits the use of the method to single slice applications. Recently, Lebel and Wilman proposed the slice-resolved extended phase graph (SEPG) fitting algorithm (17), for accurate T2 estimation from MESE data contaminated by indirect echoes. Their method is based on the extended phase graph (EPG) model proposed by Hennig (21) which provides decay curves for any given refocusing FA. The EPG model assumes perfectly rectangular slice profiles whereas the SEPG model includes the known slice profile for both excitation and refocusing pulses. The fitting algorithm fits the measurements to the SEPG model to obtain the T2 estimates. The method is robust to B1 inhomogeneity and calibration errors and it has been shown that accurate T2 estimation can be obtained from MESE data acquired with reduced FAs (<1800).
So far, the SEPG fitting algorithm has been demonstrated for fully sampled or 60% partial k-space Cartesian data. The main limitation of combining the SEPG fitting algorithm with a model-based reconstruction approach for T2 estimation from highly undersampled data (<10% sampled with respect to Nyquist sampling theorem), is the non-linearity of the SEPG model. Therefore it can be appreciated that there is a significant need for a technique to provide proper fitting with highly undersampled data. The present disclosure provides this and other advantages as will be apparent from the following detailed description and accompanying figures.